4.
\includegraphics[max width=\textwidth, alt={}, center]{c0b79c3c-9537-4c71-903b-01434dfb5d26-1_492_803_1562_452}
The diagram shows the curves \(y = ( x - 1 ) ^ { 2 }\) and \(y = 2 - \frac { 2 } { x } , x > 0\).
- Verify that the two curves meet at the points where \(x = 1\) and where \(x = 2\).
The shaded region bounded by the two curves is rotated completely about the \(x\)-axis.
- Find the exact volume of the solid formed.